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A pulsed optical absorption spectroscopy study of wide band-gap optical materials
Optical Materials 34 (2012) 2030–2034
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
A pulsed optical absorption spectroscopy study of wide band-gap optical materials I.N. Ogorodnikov a,⇑, M.S. Kiseleva a, V.Yu. Yakovlev b a b
Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia Tomsk Polytechnic University, 30 Lenina Avenue, 634050 Tomsk, Russia
a r t i c l e
i n f o
Article history: Available online 1 April 2012 Keywords: Spectroscopy with time resolution Luminescent materials Transient optical absorption Decay kinetics
a b s t r a c t The paper presents the results of a study on the formation and evolution of short-lived radiation-induced defects in wide band-gap optical materials with the mobile cations. The spectra and decay kinetics of transient optical absorption (TOA) of radiation defects in crystals of potassium and ammonium dihydro phosphates (KH2PO4 and NH4H2PO4) were studied by means of the method of pulsed optical absorption spectroscopy with the nanosecond time resolution under excitation with an electron-beam (250 keV, 10 ns). A model of electron tunneling between the electron and hole centers under conditions of the thermally stimulated mobility of one of the recombination process partners was developed. The model describes all the features of the induced optical density relaxation kinetics observed in nonlinear optical crystals KH2PO4 and NH4H2PO4 in a broad decay-time range of 10 ns–10 s after the pulse of radiation exposure. The paper discusses the origin of radiation defects that determine the TOA, as well as the dependence of the decay kinetics of the TOA on the temperature, excitation power and other experimental conditions. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Crystals of lithium borates (LiB3O5 (LBO), Li2B4O7 (LTB), Li6Gd (BO3)3 (LGBO)) and dihydro phosphates of potassium and ammonium (KH2PO4 (KDP), NH4H2PO4 (ADP)) are wide bandgap optical materials containing mobile cations. These compounds are studied intensively in recent years, both in terms of fundamental properties, and in terms of their practical applications as optical materials operating in a broad spectral range from the visible to the vacuum ultraviolet region. These materials are widely used in nonlinear and integrated optics, in laser technology, as well as they are used as detectors and transformers of ionizing radiation. Despite the differences in chemical compositions, these materials are combined a number of common properties. They have low symmetry of the crystal lattices and complex elementary cells. All these compounds contain the boron–oxygen or dihydrogen phosphate anionic groups. A distinctive feature of these compounds is the sharp contrast between the strong covalent bonds inside the anionic groups and the relatively weak ionic bonds between cations and the anionic group. The presence of a weakly bound sublattice of cations in combination with the rigid anionic framework should seriously affect on the electronic excitations dynamics and the peculiarities of radiation defects creation. This problem is acute for the case of
⇑ Corresponding author. E-mail address: [email protected] (I.N. Ogorodnikov). 0925-3467/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optmat.2012.03.010
the lightweight mobile cations of small radius in crystals of lithium borates, potassium and ammonium dihydro phosphates. However, despite the obvious importance of this phenomenon, a systematic study of the formation and evolution of short-living radiation-induced defects in these crystals was not carried out before our research. Especially it concerns the nanosecond time-range. Only few works were known in this field. Davis et al. have found that irradiation of the KDP crystal by the powerful (GW cm2) 266 nm laser pulse at room temperature results in formation of a broad band of transient optical absorption (TOA), which overlaps a large portion of the visible and the near ultraviolet region [1]. Marshall et al. have performed a semi-quantitative measurement of the TOA decay kinetics in the KDP crystal and they estimated also the effect of TOA on generation of the fourth-harmonics in this crystal [2]. Pirogova et al. have measured the TOA of the KDP crystal under excitation by an electron beam of microsecond duration [3]. We have previously investigated the TOA of crystals with a sublattice of mobile lithium (LTB [4], LBO [5], LGBO [6,7]) and hydrogen (ADP and KDP [8]) cations. For these crystals it has been experimentally revealed that the TOA decay kinetics in the timerange from 10 ns to 10 s was controlled by the electron tunneling under conditions of the thermally stimulated cation mobility. However, a detailed quantitative study of the electron tunneling decay kinetics under conditions of cations mobility in these crystals has not yet been carried out. The main goal of this work is a study of the electron tunneling decay kinetics in terms of cations mobility. In this paper we will concentrate on the mathematical modeling in comparison with
I.N. Ogorodnikov et al. / Optical Materials 34 (2012) 2030–2034
experimental results on TOA of crystals ADP and KDP in the visible and ultraviolet regions of the spectrum under excitation by an electron beam of nanosecond duration.
2. Experimental details: technique and results In the present work, we have examined the KDP and ADP crystals of high optical quality grown at the Issyk-Kul State University (Karakol, Kyrgyzstan) [9]. The samples were plane-parallel transparent plates measuring 6 5 1 mm3. The experimental setup and the main characteristics of the luminescence and absorption spectroscopy with a nanosecondscale time-resolution employed are described in considerable details in Ref. [10]. The electron-beam accelerator had the following parameters: average electron energy was 0.25 MeV; pulse duration, which is adjustable in the range of 3–15 ns, was 10 ns; current density in the pulse was 1000 A cm2, and the maximum energy density of a pulse was 160 mJ cm2. The pulse energy density used for excitation was usually either 23% or 12% of the maximum level. Registration system recorded the temporal behavior of the optical density D(t) after exposure of a crystal to a radiation pulse at the time moment t = 0. The optical density was expressed by D(t) = log10(I0/I(t)) where I0 is the intensity of a probe light transmitted through the crystal before irradiation, and I(t) is the temporal behavior of the probe light intensity after exposure to a radiation pulse. After each pulse, we checked the relaxation of the optical density until the initial level, to ensure no permanent damage to the crystal. Fig. 1 presents the time-resolved TOA spectra of ADP and KDP measured immediately after the termination of the excitation pulse and 10 ls later. The spectra of both crystals have a similar structure and consist of partially overlapping bands of Gaussian shape in the energy region of 1.5–5.5 eV. All the parts in the time-resolved TOA spectra decay homogeneously over the examined spectral region, reproducing the original shape of the spectra. The TOA decay kinetics will be discussed in Section 4, here we only note that within about 100 s after each pulse of radiation, we ob-
a
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served a complete recovery of the initial optical density of the crystal. This indicates a lack of permanent damage to the crystal during the spectroscopic measurements. In fact, the spectroscopic measurements require only 10–100 pulses of radiation, whereas the permanent damage to the crystal occurs at a much larger number of radiation pulses, see e.g. [11]. 3. Theory and modeling Let us consider a system consisting of two types of defects. The first group (A-type defects) consists of the trapped hole centers in the form of a cation vacancy captured an additional hole. The second group (B-type defects) includes the trapped electron centers in the form of a mobile interstitial cation captured an electron. Tunneling electron transfer between B and A defects leads to their disappearance as a result of recharging. It is known [12] that in general case the kinetics of the electron tunneling in a system of mobile reagents can be described by the kinetic Eq. (1) for the correlation function of dissimilar defects Y(r, t). In the linear approximation to describe the recombination process dynamics for two types of defects A + B ? 0 it is possible to consider only the macroscopic concentrations of these defects (nA, nB) and the correlation functions of dissimilar defects Y(r, t).
@Yðr; tÞ ¼ rDAB rYðr; tÞ WðrÞ Yðr; tÞ; @t
ð1Þ
where DAB is the relative diffusion coefficient, m2/s; r is interdefect distance, m; t is decay time, s; W is probability of the defect disappearance in recombination process, s1. For distant reactions in particular electron tunneling, we have the equation
WðrÞ ¼ W 0 expðr=aB Þ;
ð2Þ
where aB is half the Bohr radius of the wavefunction of the electron center and W0 is a constant. For contact reactions the alternative mechanism of defect disappearance has the probability
WðrÞ ¼ W 0 Hðr r0 Þ;
ð3Þ
where H is the Heaviside step function and r0 is the annihilation radius. The initial and boundary conditions for this equation: Y(r0, t) = 0; Y(1, t) = 1; Y(r,0) = 1 + f(r)/n0, where n0 is the initial concentration of defects; f(r) = (1/b) exp(r/b) is the spatial distribution within the pairs of defects as the exponential function of the relative distance, r; b is half the mean distance between defects. The f(r) function should be normalized:
Z
1
f ðrÞ dr ¼ 1:
ð4Þ
0
b
The time-dependent reaction rate constant is governed by the equation:
KðtÞ ¼
Z
WðrÞ Yðr; tÞ dV:
ð5Þ
V
Bimolecular stage of interaction of defects, i.e. recombination between different pairs of defects, can be described by the kinetic Eq. (6) for the macroscopic concentrations
dnA ðtÞ ¼ KðtÞ nA ðtÞ nB ðtÞ: dt
Fig. 1. TOA spectra of ADP – (a) and KDP – (b) measured at 290 K immediately after the end of the excitation pulse – (1) and 10 ls thereafter – (2). Circles are experimental data and solid lines are fitting by a sum of Gaussians.
ð6Þ
The solutions of Eqs. (1) and (6) were performed numerically using the Crank–Nicholson finite-difference scheme in a spherical coordinate system. This finite-difference scheme has a better convergence, but each step requires the solution of three-point finite-difference equations. In the present work the equations were solved numerically using the software [13].
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4. Discussion Our earlier experimental results on pulsed absorption spectroscopy of crystals ADP and KDP [9,8,14] qualitatively indicate that the transition optical absorption in them is took place due to optical transitions between the states of the valence band and local levels of the trapped hole centers. Relaxation kinetics of the radiation induced optical density over a broad time-range is controlled by the process of electron tunneling between the electron and hole centers. In the KDP and ADP crystals hole centers are identified as polaron type A-radical (a hole localized on the hydrogen vacancy) and B-radical (self-trapped hole) [15–18]. The trapped electron H0center in KDP and ADP is an interstitial hydrogen atom [19]. Data on the diffusion and electrical conductivity of crystals KDP and ADP indicate that at 290 K H0-centers in them are mobile and the thermally stimulated migration takes place [21,20]. This gives reason to discuss the decay kinetics of the TOA in KDP and ADP in the model of electron tunneling under conditions of the thermally stimulated mobility of cations. Figs. 2 and 3 present the simulation results of electron tunneling kinetics under conditions of the diffusion-controlled mobility of defects in ADP. The pair correlation functions of dissimilar defects Y(r, t) at selected decay-times t, as well as the temporal behavior of the reaction rate constants K(t) and the concentrations of defects n(t) for various calculation parameters are represented on these figures. From the Smakula’s formula it follows that the induced optical density recorded in the experiment is proportional to the actual concentration of defects. In this connection, the TOA decay kinetics up to a scale factor is comparable with the profile of the decay kinetics of the defect concentration n(t). Fig. 3 shows a comparison of the calculated values of n(t) with the experimental data on the TOA decay kinetics for ADP crystals measured at room temperature in the visible and ultraviolet spectral regions. In the decay-time range of 107–1 s the n(t) kinetics plotted in the log–log coordinates is represented by a straight line with decreasing slope p = 0.12. This is consistent with the empirical power-law decay of tunneling recombination process, n(t) tp. In the range of decay times of 107–103 s the power law describes adequately the experimental data, Fig. 3. The mobility of defects leads to a distortion of the recombination front: the maximum of the function Y(r, t) (curves 1–9 in Fig. 2a and b) corresponds to large movements in space. The tunneling process dominates at short decay times, whereas the diffusion-controlled reaction plays the crucial role at the long decay times.
Fig. 2. The correlation function of dissimilar defects Y(r, t) for ADP at 290 K. Calculation parameters: D0 = 4 107 m2/s; E = 0.48 eV; W0 = 1 107 s1; aB = 1.5 nm.
a
b
Fig. 3. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b) calculated for ADP at 290 K. The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the open circles depict the experimental data, the dash line represents approximation with the power law.
Figs. 4 and 5 present the results of calculation for KDP in comparison with the experimental data on TOA measured under the same experimental conditions. The KDP crystal has a much smaller diffusion coefficient [21,20]. In this connection, some distortion of the recombination front in the tunneling process occurs only at sufficiently long decay times, Fig. 4. For both crystals, the distortion of the recombination front on the set of correlation functions of Y(r, t) corresponds to beginning a deviation of n(t) away from the straight line followed by a subsequent exponential decrease, which is observed experimentally, Figs. 3 and 5. For the curve of the reaction rate constant K(t), this corresponds to the transition from the rapid decline to a stationary level at long decay times. In other words, the time-dependent function of the
Fig. 4. The correlation function of dissimilar defects Y(r, t) for KDP at 290 K. Calculation parameters: D0 = 3 109 m2/s; E = 0.53 eV; W0 = 1 107 s1; aB = 1.5 nm.
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a
a
b
b
Fig. 5. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b) for KDP at 290 K measured after electron-beam excitation at 23% – (1) and 12.3% – (2) power levels. The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the open and filled circles depict the experimental data.
reaction rate constant K(t) turns into a time-independent constant. From the results of calculation it follows that for greater mobility of defects, more rapid ending of the transition process occurs, that leads to steady-state kinetics of the recombination process. For ADP and KDP crystals, this corresponds to the decay times of 102 and 10 s, respectively. Almost all observed at 290 K features of the TOA decay kinetics can be explained in terms of the temporal behavior peculiarities of the reaction rate function K(t). However, the experimentally observed dependence of the TOA decay kinetics on the intensity of the excitation pulse, corresponding to different initial concentrations of defects created, cannot be explained by the peculiarities of the function K(t). The function of the reaction rate constant according to the calculation does not depend on the initial concentration of defects. The dependence of the kinetics of n(t) on the initial defect concentration n0 with the same K(t) follows directly from the Eq. (6): according to calculations with increasing initial concentration of defects twice the value of the exponent p increases from 0.12 to 0.16, Fig. 5. One can see from Figs. 2–5, the present model is in a good agreement with our experimental data obtained by the method of the pulsed optical absorption spectroscopy with the nanosecond time resolution. Decay kinetics of the TOA in the range from 107 to 10 s at 290 K is adequately described by a model of electron tunneling in the conditions of the thermally stimulated mobility of one or both of the recombining reagents. This gives grounds to discuss the temperature dependence of the TOA decay kinetics. The diffusion coefficient in Eq. (1) depends on temperature.
DAB ðTÞ ¼ D0 expðE=kb TÞ;
ð7Þ
where D0 is a constant, m2/s; E is activation energy for diffusion, eV; kb is the Boltzmann’s constant; T is temperature, K. The diffusion coefficient values for KDP and ADP for the wide temperature range are given in Refs. [21,20]. Fig. 6 presents the results of calculation for the temperature range of 200–500 K, carried out under the
Fig. 6. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b). Calculation parameters: D0 = 4 107; E = 0.48 eV; W0 = 1 107; aB = 1.5 nm; T = 200 – (1); 250 – (2); 290 – (3); 350 – (4); 400 – (5); 500 K – (6). The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the circles depict the experimental data on the TOA decay kinetics measured for ADP at 290 K.
assumption of temperature independence of the initial defect concentration n0, created by a radiation pulse. From these results it follows that at 200 K the reaction rate constant K(t) in double logarithmic coordinates decreases with time almost linearly, the curve 1 in Fig. 6a. Indeed, the probability of electron tunneling W(r) is exponentially dependent on the interdefect distance r. Close pairs of defects with the highest values W(r) recombined first. The recombination front moves with a time to longer distances r, it characterized by lower values of W(r), which accounts for observed decrease of reaction rate function K(t) with a decay time. An increase in the diffusion coefficient with increase in temperature shifts the distribution of defects to the region of smaller distances r. This results in some compensation of the reaction rate constant falls at the longer decay times, curves 2–4 in Fig. 6a. At higher temperatures there is a complete compensation of the fall of the reaction rate constant and the dependence of K(t) comes to a constant level (rate constant), corresponding to completion of the transition kinetics, curves 5 and 6 in Fig. 6a. Temperature dependence of the defect recombination kinetics in (6) for a constant n0 is completely determined by the temperature dependence of the reaction rate constant K(t), Fig. 6b. Lowtemperature kinetics in double logarithmic coordinates is represented by decreasing straight line which slope is determined by n0. As the temperature increases, the decay kinetics at long times deviate from the straight line and turns into a fast exponential decay. The higher the temperature, the faster exponential decay occurs, Fig. 6b. It is obvious that the activation energy, determined by the position of exponential decay kinetics would be consistent with a diffusion process. This agrees completely with the experimental data [9,8,14,22]. However, the initial part of the calculated kinetics in Fig. 6, b at all temperatures shows the constant negative slope. In the experiment, there is a different situation: with increasing temperature the slope of the initial part of the TOA decay kinetics in double
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logarithmic coordinates increases in absolute value with an activation energy corresponding to that for the diffusion process [9,8,14,22]. In light of the developed model, this means that under pulsed radiation exposure, the initial defect concentration n0 is really dependent on temperature. In fact, from general considerations one can assume that the pulsed radiation exposure causes the formation of close pairs of antimorphous defects ‘vacancy– interstitial ion’. With a high probability of recombination in close pairs, the probability of survival of these defects depends on the mobility of interstitial ions. As the temperature increases the mobility also increases, which leads to an increase in the number of survivors defects, i.e. to increase with temperature in the initial defect concentration n0. 5. Conclusion In present paper we investigated the kinetics of electron tunneling under conditions of the thermally stimulated mobility of recombination partners for nonlinear optical crystals KDP and ADP by means of mathematical modeling. We developed the mathematical formalism and carried out the numerical simulation. Comparison of the calculated and experimental data on TOA of crystals KDP and ADP in the visible and ultraviolet spectral regions based on known literature data allows us to formulate the following conclusions. 1. Pulsed radiation exposure leads to the formation in KDP and ADP the polaron type hole centers (A-radical – a localized hole on the vacancy of hydrogen and B-radical – self-trapped hole) and the electron trapped centers (H0-center – an interstitial hydrogen atom). Transient optical absorption occurs due to optical transitions between the valence band states and the local levels of the hole trapped centers. 2. We developed a model of the tunneling electron transport between the electron and hole trapped centers under conditions of the thermally stimulated mobility of one of the recombination process partners. The model adequately describes all features of the induced optical density relaxation kinetics observed after pulsed exposure of radiation in KDP and ADP crystals in a broad decay-time region of 10 ns–10 s. 3. The TOA decay kinetics consists of two characteristic regions. The initial part of the process is controlled by electron tunneling and its approximation can be done by the tunneling recombination law for the frozen system of defects. The ultimate part of the decay kinetics is controlled mainly by the diffusion process and it results in the rapid exponential decay of intensity. With increasing temperature, the exponential plot is shifted to shorter decay times. Thermally stimulated ‘shortening’ of the decay kinetics is characterized by an activation energy corresponding to the diffusion-controlled process. 4. The complex behavior of the reaction rate function K(t) throughout the observed region of decay times indicates the presence of transient diffusion-controlled tunnel recharging of the defects. In this case we dealing with transitional decay kinetics and simple asymptotic formula (for example, the Becquerel law) cannot be used to describe such kinetics. 5. In isothermal conditions, the negative slope of the TOA decay kinetics in log–log scale increases with increasing of the excitation pulse intensity. The reason is increasing of the initial defect density n0. The function of the reaction rate constant K(t) remains unchanged.
6. With increasing temperature, there is an increase of the initial defect concentration n0, created by the excitation pulse of constant intensity. Temperature dependence of the negative slope in the initial part of the TOA decay kinetics in log–log scale is characterized by an activation energy corresponding to the main process controlling the accumulation of defects during the exciting pulse. In crystals with the mobile cations above room temperature the diffusion serves as such process. Therefore, the activation energy determined from the temperature dependence of the initial part of the kinetics corresponds to that for the diffusion process. It is important to emphasize that the developed model is also applicable to describe the TOA decay kinetics in any other complex system with mobile cations, such as lithium borate crystals LiB3O5, Li2B4O7, and Li6Gd (BO3)3 wide bandgap optical materials. In this regard, the above conclusions are fairly general. Acknowledgment The authors thank Dr. M.M. Kidibaev for providing the samples of dihydro phosphate crystals. References [1] J.E. Davis, R.S. Hughes, H.W.H. Lee, Chem. Phys. Lett. 207 (1993) 540. [2] C.D. Marshall, S.A. Payne, M.A. Henesian, J.A. Speth, H.T. Powell, J. Opt. Soc. Am. B 11 (1994) 774. [3] G.N. Pirogova, Yu.V. Voronin, V.E. Kritskaya, A.I. Ryabov, N.A. Malov, Izv. AN SSSR. Neorgan. Materialy 22 (1986) 115. [4] I.N. Ogorodnikov, V.Yu. Yakovlev, A.V. Kruzhalov, L.I. Isaenko, Phys. Solid State 44 (2002) 1085. [5] I.N. Ogorodnikov, V.Yu. Yakovlev, L.I. Isaenko, Phys. Solid State 45 (2003) 845. [6] I.N. Ogorodnikov, N.E. Poryva, V.A. Pustovarov, A.V. Tolmachev, R.P. Yavetski, V.Yu. Yakovlev, Phys. Solid State 51 (2009) 1160. [7] I.N. Ogorodnikov, N.E. Poryvay, V.A. Pustovarov, A.V. Tolmachev, R.P. Yavetskiy, V.Yu. Yakovlev, Radiat. Meas. 45 (2010) 336. [8] I.N. Ogorodnikov, V.Yu. Yakovlev, B.V. Shulgin, M.K. Satybaldieva, Phys. Solid State 44 (2002) 880. [9] V.T. Kuanyshev, T.A. Belykh, I.N. Ogorodnikov, B.V. Shulgin, M.K. Satybaldieva, M.M. Kidibaev, Radiat. Meas. 33 (2001) 503. [10] V.Yu. Yakovlev, Sov. Phys. Solid State 34 (1992) 651. [11] I.N. Ogorodnikov, V.Yu. Ivanov, A.Yu. Kuznetsov, A.V. Kruzhalov, V.A. Maslov, Tech. Phys. Lett. 19 (1993) 325. [12] E.A. Kotomin, V.N. Kuzovkov, Modern Aspects of Diffusion-Controlled Reactions: Cooperative Phenomena in Bimolecular Processes, Elsevier, North Holland, 1996. [13] M.S. Kiseleva, I.N. Ogorodnikov, Certificate of State Registration of Computer Software (Ru N2011616814, 01.09.2011). [14] I.N. Ogorodnikov, V.Yu. Yakovlev, Phys. Status Solidi (c) 2 (2005) 641. [15] K.T. Stevens, N.Y. Garces, L.E. Halliburton, M. Yan, N.P. Zaitseva, J.J. De Yoreo, G.C. Catella, J.R. Luken, Appl. Phys. Lett. 75 (1999) 1503. [16] N.Y. Garces, K.T. Stevens, L.E. Halliburton, S.G. Demos, H.B. Radousky, N.P. Zaitseva, J. Appl. Phys. 89 (2001) 47. [17] I.N. Ogorodnikov, M. Kirm, V.A. Pustovarov, V.S. Cheremnykh, Radiat. Meas. 38 (2004) 331. [18] I.N. Ogorodnikov, V.A. Pustovarov, M. Kirm, V.S. Cheremnykh, J. Luminesc. 115 (2005) 69. [19] S.D. Setzler, K.T. Stevens, L.E. Halliburton, M. Yan, N.P. Zaitseva, J.J. De Yoreo, Phys. Rev. B: Cond. Matter. 57 (1998) 2643. [20] L.B. Harris, G.J. Vella, J. Chem. Phys. 58 (1971) 4550. [21] J.M. Pollock, M. Sharan, J. Chem. Phys. 51 (1969) 3604. [22] I.N. Ogorodnikov, V.Yu. Yakovlev, Izv. Vuzov, Physica. 54 (1/3) (2011) 137. In Russian.
Contents lists available at SciVerse ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
A pulsed optical absorption spectroscopy study of wide band-gap optical materials I.N. Ogorodnikov a,⇑, M.S. Kiseleva a, V.Yu. Yakovlev b a b
Ural Federal University, 19 Mira Street, 620002 Ekaterinburg, Russia Tomsk Polytechnic University, 30 Lenina Avenue, 634050 Tomsk, Russia
a r t i c l e
i n f o
Article history: Available online 1 April 2012 Keywords: Spectroscopy with time resolution Luminescent materials Transient optical absorption Decay kinetics
a b s t r a c t The paper presents the results of a study on the formation and evolution of short-lived radiation-induced defects in wide band-gap optical materials with the mobile cations. The spectra and decay kinetics of transient optical absorption (TOA) of radiation defects in crystals of potassium and ammonium dihydro phosphates (KH2PO4 and NH4H2PO4) were studied by means of the method of pulsed optical absorption spectroscopy with the nanosecond time resolution under excitation with an electron-beam (250 keV, 10 ns). A model of electron tunneling between the electron and hole centers under conditions of the thermally stimulated mobility of one of the recombination process partners was developed. The model describes all the features of the induced optical density relaxation kinetics observed in nonlinear optical crystals KH2PO4 and NH4H2PO4 in a broad decay-time range of 10 ns–10 s after the pulse of radiation exposure. The paper discusses the origin of radiation defects that determine the TOA, as well as the dependence of the decay kinetics of the TOA on the temperature, excitation power and other experimental conditions. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Crystals of lithium borates (LiB3O5 (LBO), Li2B4O7 (LTB), Li6Gd (BO3)3 (LGBO)) and dihydro phosphates of potassium and ammonium (KH2PO4 (KDP), NH4H2PO4 (ADP)) are wide bandgap optical materials containing mobile cations. These compounds are studied intensively in recent years, both in terms of fundamental properties, and in terms of their practical applications as optical materials operating in a broad spectral range from the visible to the vacuum ultraviolet region. These materials are widely used in nonlinear and integrated optics, in laser technology, as well as they are used as detectors and transformers of ionizing radiation. Despite the differences in chemical compositions, these materials are combined a number of common properties. They have low symmetry of the crystal lattices and complex elementary cells. All these compounds contain the boron–oxygen or dihydrogen phosphate anionic groups. A distinctive feature of these compounds is the sharp contrast between the strong covalent bonds inside the anionic groups and the relatively weak ionic bonds between cations and the anionic group. The presence of a weakly bound sublattice of cations in combination with the rigid anionic framework should seriously affect on the electronic excitations dynamics and the peculiarities of radiation defects creation. This problem is acute for the case of
⇑ Corresponding author. E-mail address: [email protected] (I.N. Ogorodnikov). 0925-3467/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optmat.2012.03.010
the lightweight mobile cations of small radius in crystals of lithium borates, potassium and ammonium dihydro phosphates. However, despite the obvious importance of this phenomenon, a systematic study of the formation and evolution of short-living radiation-induced defects in these crystals was not carried out before our research. Especially it concerns the nanosecond time-range. Only few works were known in this field. Davis et al. have found that irradiation of the KDP crystal by the powerful (GW cm2) 266 nm laser pulse at room temperature results in formation of a broad band of transient optical absorption (TOA), which overlaps a large portion of the visible and the near ultraviolet region [1]. Marshall et al. have performed a semi-quantitative measurement of the TOA decay kinetics in the KDP crystal and they estimated also the effect of TOA on generation of the fourth-harmonics in this crystal [2]. Pirogova et al. have measured the TOA of the KDP crystal under excitation by an electron beam of microsecond duration [3]. We have previously investigated the TOA of crystals with a sublattice of mobile lithium (LTB [4], LBO [5], LGBO [6,7]) and hydrogen (ADP and KDP [8]) cations. For these crystals it has been experimentally revealed that the TOA decay kinetics in the timerange from 10 ns to 10 s was controlled by the electron tunneling under conditions of the thermally stimulated cation mobility. However, a detailed quantitative study of the electron tunneling decay kinetics under conditions of cations mobility in these crystals has not yet been carried out. The main goal of this work is a study of the electron tunneling decay kinetics in terms of cations mobility. In this paper we will concentrate on the mathematical modeling in comparison with
I.N. Ogorodnikov et al. / Optical Materials 34 (2012) 2030–2034
experimental results on TOA of crystals ADP and KDP in the visible and ultraviolet regions of the spectrum under excitation by an electron beam of nanosecond duration.
2. Experimental details: technique and results In the present work, we have examined the KDP and ADP crystals of high optical quality grown at the Issyk-Kul State University (Karakol, Kyrgyzstan) [9]. The samples were plane-parallel transparent plates measuring 6 5 1 mm3. The experimental setup and the main characteristics of the luminescence and absorption spectroscopy with a nanosecondscale time-resolution employed are described in considerable details in Ref. [10]. The electron-beam accelerator had the following parameters: average electron energy was 0.25 MeV; pulse duration, which is adjustable in the range of 3–15 ns, was 10 ns; current density in the pulse was 1000 A cm2, and the maximum energy density of a pulse was 160 mJ cm2. The pulse energy density used for excitation was usually either 23% or 12% of the maximum level. Registration system recorded the temporal behavior of the optical density D(t) after exposure of a crystal to a radiation pulse at the time moment t = 0. The optical density was expressed by D(t) = log10(I0/I(t)) where I0 is the intensity of a probe light transmitted through the crystal before irradiation, and I(t) is the temporal behavior of the probe light intensity after exposure to a radiation pulse. After each pulse, we checked the relaxation of the optical density until the initial level, to ensure no permanent damage to the crystal. Fig. 1 presents the time-resolved TOA spectra of ADP and KDP measured immediately after the termination of the excitation pulse and 10 ls later. The spectra of both crystals have a similar structure and consist of partially overlapping bands of Gaussian shape in the energy region of 1.5–5.5 eV. All the parts in the time-resolved TOA spectra decay homogeneously over the examined spectral region, reproducing the original shape of the spectra. The TOA decay kinetics will be discussed in Section 4, here we only note that within about 100 s after each pulse of radiation, we ob-
a
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served a complete recovery of the initial optical density of the crystal. This indicates a lack of permanent damage to the crystal during the spectroscopic measurements. In fact, the spectroscopic measurements require only 10–100 pulses of radiation, whereas the permanent damage to the crystal occurs at a much larger number of radiation pulses, see e.g. [11]. 3. Theory and modeling Let us consider a system consisting of two types of defects. The first group (A-type defects) consists of the trapped hole centers in the form of a cation vacancy captured an additional hole. The second group (B-type defects) includes the trapped electron centers in the form of a mobile interstitial cation captured an electron. Tunneling electron transfer between B and A defects leads to their disappearance as a result of recharging. It is known [12] that in general case the kinetics of the electron tunneling in a system of mobile reagents can be described by the kinetic Eq. (1) for the correlation function of dissimilar defects Y(r, t). In the linear approximation to describe the recombination process dynamics for two types of defects A + B ? 0 it is possible to consider only the macroscopic concentrations of these defects (nA, nB) and the correlation functions of dissimilar defects Y(r, t).
@Yðr; tÞ ¼ rDAB rYðr; tÞ WðrÞ Yðr; tÞ; @t
ð1Þ
where DAB is the relative diffusion coefficient, m2/s; r is interdefect distance, m; t is decay time, s; W is probability of the defect disappearance in recombination process, s1. For distant reactions in particular electron tunneling, we have the equation
WðrÞ ¼ W 0 expðr=aB Þ;
ð2Þ
where aB is half the Bohr radius of the wavefunction of the electron center and W0 is a constant. For contact reactions the alternative mechanism of defect disappearance has the probability
WðrÞ ¼ W 0 Hðr r0 Þ;
ð3Þ
where H is the Heaviside step function and r0 is the annihilation radius. The initial and boundary conditions for this equation: Y(r0, t) = 0; Y(1, t) = 1; Y(r,0) = 1 + f(r)/n0, where n0 is the initial concentration of defects; f(r) = (1/b) exp(r/b) is the spatial distribution within the pairs of defects as the exponential function of the relative distance, r; b is half the mean distance between defects. The f(r) function should be normalized:
Z
1
f ðrÞ dr ¼ 1:
ð4Þ
0
b
The time-dependent reaction rate constant is governed by the equation:
KðtÞ ¼
Z
WðrÞ Yðr; tÞ dV:
ð5Þ
V
Bimolecular stage of interaction of defects, i.e. recombination between different pairs of defects, can be described by the kinetic Eq. (6) for the macroscopic concentrations
dnA ðtÞ ¼ KðtÞ nA ðtÞ nB ðtÞ: dt
Fig. 1. TOA spectra of ADP – (a) and KDP – (b) measured at 290 K immediately after the end of the excitation pulse – (1) and 10 ls thereafter – (2). Circles are experimental data and solid lines are fitting by a sum of Gaussians.
ð6Þ
The solutions of Eqs. (1) and (6) were performed numerically using the Crank–Nicholson finite-difference scheme in a spherical coordinate system. This finite-difference scheme has a better convergence, but each step requires the solution of three-point finite-difference equations. In the present work the equations were solved numerically using the software [13].
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4. Discussion Our earlier experimental results on pulsed absorption spectroscopy of crystals ADP and KDP [9,8,14] qualitatively indicate that the transition optical absorption in them is took place due to optical transitions between the states of the valence band and local levels of the trapped hole centers. Relaxation kinetics of the radiation induced optical density over a broad time-range is controlled by the process of electron tunneling between the electron and hole centers. In the KDP and ADP crystals hole centers are identified as polaron type A-radical (a hole localized on the hydrogen vacancy) and B-radical (self-trapped hole) [15–18]. The trapped electron H0center in KDP and ADP is an interstitial hydrogen atom [19]. Data on the diffusion and electrical conductivity of crystals KDP and ADP indicate that at 290 K H0-centers in them are mobile and the thermally stimulated migration takes place [21,20]. This gives reason to discuss the decay kinetics of the TOA in KDP and ADP in the model of electron tunneling under conditions of the thermally stimulated mobility of cations. Figs. 2 and 3 present the simulation results of electron tunneling kinetics under conditions of the diffusion-controlled mobility of defects in ADP. The pair correlation functions of dissimilar defects Y(r, t) at selected decay-times t, as well as the temporal behavior of the reaction rate constants K(t) and the concentrations of defects n(t) for various calculation parameters are represented on these figures. From the Smakula’s formula it follows that the induced optical density recorded in the experiment is proportional to the actual concentration of defects. In this connection, the TOA decay kinetics up to a scale factor is comparable with the profile of the decay kinetics of the defect concentration n(t). Fig. 3 shows a comparison of the calculated values of n(t) with the experimental data on the TOA decay kinetics for ADP crystals measured at room temperature in the visible and ultraviolet spectral regions. In the decay-time range of 107–1 s the n(t) kinetics plotted in the log–log coordinates is represented by a straight line with decreasing slope p = 0.12. This is consistent with the empirical power-law decay of tunneling recombination process, n(t) tp. In the range of decay times of 107–103 s the power law describes adequately the experimental data, Fig. 3. The mobility of defects leads to a distortion of the recombination front: the maximum of the function Y(r, t) (curves 1–9 in Fig. 2a and b) corresponds to large movements in space. The tunneling process dominates at short decay times, whereas the diffusion-controlled reaction plays the crucial role at the long decay times.
Fig. 2. The correlation function of dissimilar defects Y(r, t) for ADP at 290 K. Calculation parameters: D0 = 4 107 m2/s; E = 0.48 eV; W0 = 1 107 s1; aB = 1.5 nm.
a
b
Fig. 3. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b) calculated for ADP at 290 K. The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the open circles depict the experimental data, the dash line represents approximation with the power law.
Figs. 4 and 5 present the results of calculation for KDP in comparison with the experimental data on TOA measured under the same experimental conditions. The KDP crystal has a much smaller diffusion coefficient [21,20]. In this connection, some distortion of the recombination front in the tunneling process occurs only at sufficiently long decay times, Fig. 4. For both crystals, the distortion of the recombination front on the set of correlation functions of Y(r, t) corresponds to beginning a deviation of n(t) away from the straight line followed by a subsequent exponential decrease, which is observed experimentally, Figs. 3 and 5. For the curve of the reaction rate constant K(t), this corresponds to the transition from the rapid decline to a stationary level at long decay times. In other words, the time-dependent function of the
Fig. 4. The correlation function of dissimilar defects Y(r, t) for KDP at 290 K. Calculation parameters: D0 = 3 109 m2/s; E = 0.53 eV; W0 = 1 107 s1; aB = 1.5 nm.
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a
a
b
b
Fig. 5. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b) for KDP at 290 K measured after electron-beam excitation at 23% – (1) and 12.3% – (2) power levels. The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the open and filled circles depict the experimental data.
reaction rate constant K(t) turns into a time-independent constant. From the results of calculation it follows that for greater mobility of defects, more rapid ending of the transition process occurs, that leads to steady-state kinetics of the recombination process. For ADP and KDP crystals, this corresponds to the decay times of 102 and 10 s, respectively. Almost all observed at 290 K features of the TOA decay kinetics can be explained in terms of the temporal behavior peculiarities of the reaction rate function K(t). However, the experimentally observed dependence of the TOA decay kinetics on the intensity of the excitation pulse, corresponding to different initial concentrations of defects created, cannot be explained by the peculiarities of the function K(t). The function of the reaction rate constant according to the calculation does not depend on the initial concentration of defects. The dependence of the kinetics of n(t) on the initial defect concentration n0 with the same K(t) follows directly from the Eq. (6): according to calculations with increasing initial concentration of defects twice the value of the exponent p increases from 0.12 to 0.16, Fig. 5. One can see from Figs. 2–5, the present model is in a good agreement with our experimental data obtained by the method of the pulsed optical absorption spectroscopy with the nanosecond time resolution. Decay kinetics of the TOA in the range from 107 to 10 s at 290 K is adequately described by a model of electron tunneling in the conditions of the thermally stimulated mobility of one or both of the recombining reagents. This gives grounds to discuss the temperature dependence of the TOA decay kinetics. The diffusion coefficient in Eq. (1) depends on temperature.
DAB ðTÞ ¼ D0 expðE=kb TÞ;
ð7Þ
where D0 is a constant, m2/s; E is activation energy for diffusion, eV; kb is the Boltzmann’s constant; T is temperature, K. The diffusion coefficient values for KDP and ADP for the wide temperature range are given in Refs. [21,20]. Fig. 6 presents the results of calculation for the temperature range of 200–500 K, carried out under the
Fig. 6. The reaction rate constant K(t) – (a) and the concentration n(t)/n0 – (b). Calculation parameters: D0 = 4 107; E = 0.48 eV; W0 = 1 107; aB = 1.5 nm; T = 200 – (1); 250 – (2); 290 – (3); 350 – (4); 400 – (5); 500 K – (6). The concentration n(t) is normalized to unity at n0 = 1 1023 m3; the circles depict the experimental data on the TOA decay kinetics measured for ADP at 290 K.
assumption of temperature independence of the initial defect concentration n0, created by a radiation pulse. From these results it follows that at 200 K the reaction rate constant K(t) in double logarithmic coordinates decreases with time almost linearly, the curve 1 in Fig. 6a. Indeed, the probability of electron tunneling W(r) is exponentially dependent on the interdefect distance r. Close pairs of defects with the highest values W(r) recombined first. The recombination front moves with a time to longer distances r, it characterized by lower values of W(r), which accounts for observed decrease of reaction rate function K(t) with a decay time. An increase in the diffusion coefficient with increase in temperature shifts the distribution of defects to the region of smaller distances r. This results in some compensation of the reaction rate constant falls at the longer decay times, curves 2–4 in Fig. 6a. At higher temperatures there is a complete compensation of the fall of the reaction rate constant and the dependence of K(t) comes to a constant level (rate constant), corresponding to completion of the transition kinetics, curves 5 and 6 in Fig. 6a. Temperature dependence of the defect recombination kinetics in (6) for a constant n0 is completely determined by the temperature dependence of the reaction rate constant K(t), Fig. 6b. Lowtemperature kinetics in double logarithmic coordinates is represented by decreasing straight line which slope is determined by n0. As the temperature increases, the decay kinetics at long times deviate from the straight line and turns into a fast exponential decay. The higher the temperature, the faster exponential decay occurs, Fig. 6b. It is obvious that the activation energy, determined by the position of exponential decay kinetics would be consistent with a diffusion process. This agrees completely with the experimental data [9,8,14,22]. However, the initial part of the calculated kinetics in Fig. 6, b at all temperatures shows the constant negative slope. In the experiment, there is a different situation: with increasing temperature the slope of the initial part of the TOA decay kinetics in double
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logarithmic coordinates increases in absolute value with an activation energy corresponding to that for the diffusion process [9,8,14,22]. In light of the developed model, this means that under pulsed radiation exposure, the initial defect concentration n0 is really dependent on temperature. In fact, from general considerations one can assume that the pulsed radiation exposure causes the formation of close pairs of antimorphous defects ‘vacancy– interstitial ion’. With a high probability of recombination in close pairs, the probability of survival of these defects depends on the mobility of interstitial ions. As the temperature increases the mobility also increases, which leads to an increase in the number of survivors defects, i.e. to increase with temperature in the initial defect concentration n0. 5. Conclusion In present paper we investigated the kinetics of electron tunneling under conditions of the thermally stimulated mobility of recombination partners for nonlinear optical crystals KDP and ADP by means of mathematical modeling. We developed the mathematical formalism and carried out the numerical simulation. Comparison of the calculated and experimental data on TOA of crystals KDP and ADP in the visible and ultraviolet spectral regions based on known literature data allows us to formulate the following conclusions. 1. Pulsed radiation exposure leads to the formation in KDP and ADP the polaron type hole centers (A-radical – a localized hole on the vacancy of hydrogen and B-radical – self-trapped hole) and the electron trapped centers (H0-center – an interstitial hydrogen atom). Transient optical absorption occurs due to optical transitions between the valence band states and the local levels of the hole trapped centers. 2. We developed a model of the tunneling electron transport between the electron and hole trapped centers under conditions of the thermally stimulated mobility of one of the recombination process partners. The model adequately describes all features of the induced optical density relaxation kinetics observed after pulsed exposure of radiation in KDP and ADP crystals in a broad decay-time region of 10 ns–10 s. 3. The TOA decay kinetics consists of two characteristic regions. The initial part of the process is controlled by electron tunneling and its approximation can be done by the tunneling recombination law for the frozen system of defects. The ultimate part of the decay kinetics is controlled mainly by the diffusion process and it results in the rapid exponential decay of intensity. With increasing temperature, the exponential plot is shifted to shorter decay times. Thermally stimulated ‘shortening’ of the decay kinetics is characterized by an activation energy corresponding to the diffusion-controlled process. 4. The complex behavior of the reaction rate function K(t) throughout the observed region of decay times indicates the presence of transient diffusion-controlled tunnel recharging of the defects. In this case we dealing with transitional decay kinetics and simple asymptotic formula (for example, the Becquerel law) cannot be used to describe such kinetics. 5. In isothermal conditions, the negative slope of the TOA decay kinetics in log–log scale increases with increasing of the excitation pulse intensity. The reason is increasing of the initial defect density n0. The function of the reaction rate constant K(t) remains unchanged.
6. With increasing temperature, there is an increase of the initial defect concentration n0, created by the excitation pulse of constant intensity. Temperature dependence of the negative slope in the initial part of the TOA decay kinetics in log–log scale is characterized by an activation energy corresponding to the main process controlling the accumulation of defects during the exciting pulse. In crystals with the mobile cations above room temperature the diffusion serves as such process. Therefore, the activation energy determined from the temperature dependence of the initial part of the kinetics corresponds to that for the diffusion process. It is important to emphasize that the developed model is also applicable to describe the TOA decay kinetics in any other complex system with mobile cations, such as lithium borate crystals LiB3O5, Li2B4O7, and Li6Gd (BO3)3 wide bandgap optical materials. In this regard, the above conclusions are fairly general. Acknowledgment The authors thank Dr. M.M. Kidibaev for providing the samples of dihydro phosphate crystals. References [1] J.E. Davis, R.S. Hughes, H.W.H. Lee, Chem. Phys. Lett. 207 (1993) 540. [2] C.D. Marshall, S.A. Payne, M.A. Henesian, J.A. Speth, H.T. Powell, J. Opt. Soc. Am. B 11 (1994) 774. [3] G.N. Pirogova, Yu.V. Voronin, V.E. Kritskaya, A.I. Ryabov, N.A. Malov, Izv. AN SSSR. Neorgan. Materialy 22 (1986) 115. [4] I.N. Ogorodnikov, V.Yu. Yakovlev, A.V. Kruzhalov, L.I. Isaenko, Phys. Solid State 44 (2002) 1085. [5] I.N. Ogorodnikov, V.Yu. Yakovlev, L.I. Isaenko, Phys. Solid State 45 (2003) 845. [6] I.N. Ogorodnikov, N.E. Poryva, V.A. Pustovarov, A.V. Tolmachev, R.P. Yavetski, V.Yu. Yakovlev, Phys. Solid State 51 (2009) 1160. [7] I.N. Ogorodnikov, N.E. Poryvay, V.A. Pustovarov, A.V. Tolmachev, R.P. Yavetskiy, V.Yu. Yakovlev, Radiat. Meas. 45 (2010) 336. [8] I.N. Ogorodnikov, V.Yu. Yakovlev, B.V. Shulgin, M.K. Satybaldieva, Phys. Solid State 44 (2002) 880. [9] V.T. Kuanyshev, T.A. Belykh, I.N. Ogorodnikov, B.V. Shulgin, M.K. Satybaldieva, M.M. Kidibaev, Radiat. Meas. 33 (2001) 503. [10] V.Yu. Yakovlev, Sov. Phys. Solid State 34 (1992) 651. [11] I.N. Ogorodnikov, V.Yu. Ivanov, A.Yu. Kuznetsov, A.V. Kruzhalov, V.A. Maslov, Tech. Phys. Lett. 19 (1993) 325. [12] E.A. Kotomin, V.N. Kuzovkov, Modern Aspects of Diffusion-Controlled Reactions: Cooperative Phenomena in Bimolecular Processes, Elsevier, North Holland, 1996. [13] M.S. Kiseleva, I.N. Ogorodnikov, Certificate of State Registration of Computer Software (Ru N2011616814, 01.09.2011). [14] I.N. Ogorodnikov, V.Yu. Yakovlev, Phys. Status Solidi (c) 2 (2005) 641. [15] K.T. Stevens, N.Y. Garces, L.E. Halliburton, M. Yan, N.P. Zaitseva, J.J. De Yoreo, G.C. Catella, J.R. Luken, Appl. Phys. Lett. 75 (1999) 1503. [16] N.Y. Garces, K.T. Stevens, L.E. Halliburton, S.G. Demos, H.B. Radousky, N.P. Zaitseva, J. Appl. Phys. 89 (2001) 47. [17] I.N. Ogorodnikov, M. Kirm, V.A. Pustovarov, V.S. Cheremnykh, Radiat. Meas. 38 (2004) 331. [18] I.N. Ogorodnikov, V.A. Pustovarov, M. Kirm, V.S. Cheremnykh, J. Luminesc. 115 (2005) 69. [19] S.D. Setzler, K.T. Stevens, L.E. Halliburton, M. Yan, N.P. Zaitseva, J.J. De Yoreo, Phys. Rev. B: Cond. Matter. 57 (1998) 2643. [20] L.B. Harris, G.J. Vella, J. Chem. Phys. 58 (1971) 4550. [21] J.M. Pollock, M. Sharan, J. Chem. Phys. 51 (1969) 3604. [22] I.N. Ogorodnikov, V.Yu. Yakovlev, Izv. Vuzov, Physica. 54 (1/3) (2011) 137. In Russian.